CN106625687A - Kinematics modeling method for articulated robot - Google Patents
Kinematics modeling method for articulated robot Download PDFInfo
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- CN106625687A CN106625687A CN201610970757.2A CN201610970757A CN106625687A CN 106625687 A CN106625687 A CN 106625687A CN 201610970757 A CN201610970757 A CN 201610970757A CN 106625687 A CN106625687 A CN 106625687A
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- mechanical arm
- coordinate system
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- pedestal
- joint
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Automation & Control Theory (AREA)
- Manipulator (AREA)
Abstract
The invention belongs to the field of robot modeling and provides a kinematics modeling method for an articulated robot. The method comprises the following steps that the slant angle of a tail end actuator relative to the horizontal face of a pedestal coordinate system is input; according to the lengths and slant angles of all mechanical arms and through a kinematic inverse solution, the rotating angles of all joints and a pedestal of each mechanical arm are obtained; and according to the rotating angles of all the joints and the pedestal of each mechanical arm and through a forward kinematics solution, a transformational matrix of the tail end actuator relative to the pedestal coordinate system is obtained. According to the kinematics modeling method for the articulated robot, through the slant angle of the tail end actuator relative to the horizontal face of the pedestal coordinate system and the lengths of the mechanical arms, the rotating angles of all the joints and the pedestal of each mechanical arm are obtained through the kinematic inverse solution, and the pose and position of the tail end actuator relative to the pedestal coordinate system are obtained through the forward kinematics solution; and the derivation process of the modeling method is easy and pellucid, popular and easy to understand, convenient to program and suitable for reality.
Description
Technical field
The invention belongs to robot modeling field, more particularly to a kind of articulated robot Kinematic Model method.
Background technology
Robot since coming out from the beginning of the sixties, experienced for more than 50 years as one of greatest invention of 20th century mankind
Development have been achieved for significant progress, in robot application field, the research of robot kinematics' problem is to carry out machine
The important foundation of people's Motion trajectory, motion simulation.
The Kinematic Model method of conventional machines people is to set up rectangular coordinate system in each joint of mechanical arm, it is then determined that phase
The all transition matrixes for obtaining then are multiplied final acquisition end-of-arm tooling coordinate system extremely by the transition matrix between adjacent rectangular coordinate system
The transition matrix of base coordinate system, so that it is determined that ending coordinates tie up to the position in base coordinate system and attitude.Wherein Jing the most
The modeling method of allusion quotation is DH methods, and the method is set up coordinate system, adopted by a series of regulations on each joint of robot arm
Variation relation between four variable description robot arms, the process that the method sets up coordinate system is excessively numerous and diverse, and calculates
Amount is excessive, and relative to multi-freedom robot, this problem is more projected.
The content of the invention
The embodiment of the present invention provides a kind of articulated robot Kinematic Model method, it is intended to solves DH modelings and sets up coordinate
The process of system is excessively numerous and diverse, and the excessive problem of amount of calculation.
The present invention is achieved in that a kind of articulated robot Kinematic Model method, and methods described comprises the steps：
Inclination angle of the input end effector relative to base coordinate system horizontal plane；
According to each mechanical arm brachium and the inclination angle, using Inverse Kinematics Solution turning for each joint of mechanical arm and pedestal is obtained
Angle；
According to each joint of the mechanical arm and the corner of the pedestal, using forward kinematics solution the end effector is obtained
Relative to the transformation matrix of the base coordinate system.
It is long relative to the inclination angle of pedestal coordinate horizontal plane and mechanical armed lever by end effector in the embodiment of the present invention,
The corner of each joint of mechanical arm and pedestal is obtained using Inverse Kinematics Solution, recycles forward kinematics solution to obtain end effector relative
Attitude and position in base coordinate system, this modeling method derivation is simple and clear, easy-to-understand, is easy to programming, it is adaptable to
It is actual.
Description of the drawings
Fig. 1 is the flow chart of robot kinematics' modeling method provided in an embodiment of the present invention；
Fig. 2 is the 3 mechanical arm sectional views that inventive embodiments are provided；
Fig. 3 is that the bar length of the corner and mechanical arm according to each joint of mechanical arm and pedestal provided in an embodiment of the present invention is obtained
Flow chart of the end effector relative to the transformation matrix of base coordinate system.
Specific embodiment
In order that the objects, technical solutions and advantages of the present invention become more apparent, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only to explain the present invention, and
It is not used in the restriction present invention.
It is long relative to the inclination angle of pedestal coordinate horizontal plane and mechanical armed lever by end effector in the embodiment of the present invention,
The corner of each joint of mechanical arm and pedestal is obtained using Inverse Kinematics Solution, recycles forward kinematics solution to obtain end effector relative
Attitude and position in base coordinate system, this modeling method derivation is simple and clear, easy-to-understand, is easy to programming, it is adaptable to
It is actual.
Fig. 1 is a kind of flow chart of robot kinematics' modeling method provided in an embodiment of the present invention, as follows in detail：
Step S110, is input into inclination angle of the end effector relative to base coordinate system horizontal plane；
In embodiments of the present invention, operator carried out according to robot operation needs it is relative to set end effector
In the inclination angle of base coordinate system horizontal plane, the angular range that can be chosen is 0 ° to 360 °.
Step S120, according to the brachium and end effector of each mechanical arm relative to base coordinate system horizontal plane inclination
Angle, using Inverse Kinematics Solution the corner of each joint of mechanical arm and pedestal is obtained；
In embodiments of the present invention, the 3≤L of quantity of robot arm, the optimal number of current robot arm is 3
It is individual, when mechanical arm quantity is less than 3, there is no end effector controllable state, will not select in design, mechanical arm quantity is got over
Many, end controllable state is more, also more preferable, but designs the weight for needing consideration to increase and mechanism driving etc., is unfavorable for throwing
Money is saved.
In embodiments of the present invention, when quantity L=3 of mechanical arm, the inverse solution equation in coordinates group of solution F points to O points, with
F points are obtained to the corner of each joint of mechanical arm and pedestal between O points；
When 3 ＜ L≤6 of mechanical arm quantity, F points are solved successively to P points, the inverse solution equation in coordinates group of P points to O points, with
O points are obtained to the corner of each joint of mechanical arm and pedestal between F points；
Wherein, the origin of O points basic point coordinate system, F points be end effector, P points be middle joint point (as L=5, P points
For second or the 3rd articulare).
Fig. 2 is 3 mechanical arm sectional views, is that 3 citings illustrate the inverse solution coordinate for solving F points to O points with mechanical arm quantity
Equation group, to obtain F points to the concrete reckoning process of the corner of each joint of mechanical arm and pedestal between O points：
The inclination angle that input end effector is set relative to base coordinate system horizontal plane is as 45 °, i.e. θ1+θ2+θ3=π/4,
Set up inverse solution equation in coordinates group：
Wherein, r1、r2、r3Represent that the bar of first, second, third mechanical arm is long respectively, θ1、θ2、θ3、θ4First is represented respectively
The anglec of rotation of mechanical arm, second mechanical arm, the corner of three-mechanical arm and pedestal.
Abbreviation equation group (1), can obtain：
Wherein：
Andz’+r3Sin (π/4)=b.
When the quantity of the mechanical arm is 4, using P points as origin, F points are solved to P points according to the method for equation group (1)
Between each joint of mechanical arm corner, meanwhile, then using the corner of three-mechanical arm as input inclination angle, according to equation group
(1) method solves P points to the corner of each joint of mechanical arm and pedestal between O points, so as to obtain each joint of whole mechanical arm and
The corner of pedestal.
Step S130, according to each joint of mechanical arm and the corner of pedestal, using forward kinematics solution end effector phase is obtained
For the transformation matrix of base coordinate system.
In embodiments of the present invention, held obtaining end relative to the transformation matrix of base coordinate system by end effector
Just solving equation for row device coordinate, is just solving equation and can be used to calculate each mechanical arm real-time position with respect to the horizontal plane in synchronous operation
Put, according to the corner of joint of mechanical arm so that it is determined that attitude and position of the robot arm relative to base coordinate system.
Fig. 3 is that the bar length of the corner and mechanical arm according to each joint of mechanical arm and pedestal provided in an embodiment of the present invention is obtained
End effector relative to the transformation matrix of base coordinate system flow chart, it is in detail as follows：
Step S310, according to the corner of each node of mechanical arm and pedestal base coordinate system rotational transformation matrix, pedestal are obtained
Coordinate is tied to the transformation matrix between the transformation matrix of the first body joint point coordinate system and each adjacent segment point；
Step S320, the conversion square of base coordinate system rotational transformation matrix, base coordinate system to the first body joint point coordinate system
Transformation matrix between battle array and each adjacent segment point is multiplied generates the transformation matrix of end effector opposite base coordinate system successively.
In embodiments of the present invention, illustrate by taking 3 mechanical arms in Fig. 2 as an example according to each joint of mechanical arm and pedestal
Corner obtains end effector and realizes process relative to the transformation matrix of base coordinate system,1T0、2T1、3T2、4T3Base is represented respectively
Seat coordinate system rotation transformation matrix, from base coordinate system to the transformation matrix of the first body joint point coordinate system, from the first articulare
Coordinate is tied to the transformation matrix of second joint point coordinates system and is tied to the change of end effector coordinate system from second joint point coordinates
Change matrix.
Wherein, θ4、θ1、θ2、θ3Represent respectively pedestal the anglec of rotation and first mechanical arm joint, second mechanical arm joint, the
The corner in three-mechanical arm joint,
The transformation matrix of end effector opposite base coordinate system is：4T0=1T0 2T1 3T2 4T3。
It is long relative to the inclination angle of pedestal coordinate horizontal plane and mechanical armed lever by end effector in the embodiment of the present invention,
The corner of each joint of mechanical arm and pedestal is obtained using Inverse Kinematics Solution, recycles forward kinematics solution to obtain end effector relative
Attitude and position in base coordinate system, this modeling method derivation is simple and clear, easy-to-understand, is easy to programming, it is adaptable to
It is actual.
Presently preferred embodiments of the present invention is the foregoing is only, not to limit the present invention, all essences in the present invention
Any modification, equivalent and improvement made within god and principle etc., should be included within the scope of the present invention.
Claims (4)
1. a kind of articulated robot Kinematic Model method, it is characterised in that methods described comprises the steps：
Inclination angle of the input end effector relative to base coordinate system horizontal plane；
According to each mechanical arm brachium and the inclination angle, using Inverse Kinematics Solution the corner of each joint of mechanical arm and pedestal is obtained；
According to each joint of the mechanical arm and the corner of the pedestal, the end effector is obtained using forward kinematics solution relative
In the transformation matrix of the base coordinate system.
2. articulated robot Kinematic Model method as claimed in claim 1, it is characterised in that described according to each mechanical arm arm
Long and described inclination angle, the corner for being obtained using Inverse Kinematics Solution each joint of mechanical arm and pedestal is comprised the following steps that：
When quantity L=3 of the mechanical arm, F points are solved to the inverse solution equation in coordinates group of O points, to obtain the F points to described
The corner of each joint of mechanical arm and the pedestal between O points；
When 3 ＜ L≤6 of quantity of the mechanical arm, the F points are solved successively to P points, the inverse solution of P points to the O points
Equation in coordinates group, to obtain the O points to the corner of each joint of mechanical arm and the pedestal between the F points；
Wherein, the origin of the O points basic point coordinate system, the P points are middle joint point, and the F points are end effector.
3. articulated robot Kinematic Model method as claimed in claim 1, it is characterised in that the quantity of the mechanical arm is
3。
4. articulated robot Kinematic Model method as claimed in claim 1, it is characterised in that described according to the mechanical arm
Each joint and the corner of the pedestal, obtain the end effector relative to the concrete of the transformation matrix of the base coordinate system
Following steps：
The base coordinate system rotational transformation matrix, the base are obtained according to the corner of each node of the mechanical arm and the pedestal
Seat coordinate is tied to the transformation matrix between the transformation matrix and each adjacent segment point of the first body joint point coordinate system；
The transformation matrix and institute of the base coordinate system rotational transformation matrix, the base coordinate system to the first body joint point coordinate system
State the transformation matrix between each adjacent segment point and be multiplied successively and generate the conversion of the relatively described base coordinate system of the end effector
Matrix.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107263477A (en) * | 2017-07-07 | 2017-10-20 | 浙江大学 | One kind rope driving series connection joint type Snakelike mechanical arm control method |
| CN107685330A (en) * | 2017-10-18 | 2018-02-13 | 佛山华数机器人有限公司 | A kind of Inverse Kinematics Solution method for solving of six degree of freedom wrist bias series robot |
| CN109458964A (en) * | 2018-12-24 | 2019-03-12 | 哈尔滨工程大学 | A kind of four-degree-of-freedom space to Six-freedom-degree space three-dimensional coordinate transmission method |
| CN109846411A (en) * | 2018-12-28 | 2019-06-07 | 尚一盛世(北京)科技有限公司 | A kind of climbing support arm raises angle control system |
| CN110587596A (en) * | 2019-07-30 | 2019-12-20 | 武汉恒新动力科技有限公司 | Multi-axis configuration device remote control method and device, terminal equipment and storage medium |
| CN114413807A (en) * | 2021-12-15 | 2022-04-29 | 连云港杰瑞自动化有限公司 | Dimension test method suitable for large fluid loading and unloading equipment for ship |
| CN117621053A (en) * | 2023-11-09 | 2024-03-01 | 中国矿业大学 | Modeling method for belt conveyor disassembly robot |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107263477A (en) * | 2017-07-07 | 2017-10-20 | 浙江大学 | One kind rope driving series connection joint type Snakelike mechanical arm control method |
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| CN114413807A (en) * | 2021-12-15 | 2022-04-29 | 连云港杰瑞自动化有限公司 | Dimension test method suitable for large fluid loading and unloading equipment for ship |
| CN114413807B (en) * | 2021-12-15 | 2024-01-09 | 连云港杰瑞自动化有限公司 | Size testing method suitable for marine large-scale fluid loading and unloading equipment |
| CN117621053A (en) * | 2023-11-09 | 2024-03-01 | 中国矿业大学 | Modeling method for belt conveyor disassembly robot |
| CN117621053B (en) * | 2023-11-09 | 2024-05-31 | 中国矿业大学 | Modeling method for belt conveyor disassembly robot |
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